American Economic Association

Contracts as a Barrier to Entry Author(s): Philippe Aghion and Patrick Bolton Reviewed work(s): Source: The American Economic Review, Vol. 77, No. 3 (Jun., 1987), pp. 388-401 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1804102 . Accessed: 18/01/2012 17:51 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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Contracts as a Barrierto Entry By PHILIPPE AGHION AND PATRICK BOLTON* It is shownthatan incumbent sellerwhofaces a threatof entryintohis or her marketwill sign long-term contractsthatpreventthe entryof some lower-cost producerseventhoughtheydo notprecludeentrycompletely. Moreover,whena sellerpossessessuperiorinformation aboutthelikelihoodofentry, it is shownthat thelengthof thecontractmayact as a signalof thetrueprobability ofentry. Most of the literatureon entryprevention deals with the case of two duopolists(the established firmand the potentialentrant) who compete with each other to share a market,where one of the duopolists (the incumbent)has a first-move advantage.'This basic paradigmhas been studiedundervarious assumptions:about thestrategy space of the players; the information structure of the game; and the time horizon.Recently,the model has been enlargedto allow forseveral entrants,several incumbents,several markets,and thirdparties.2 We propose here to extendthe entry-preventionmodel in one otherdirection,which to our knowledgehas not yet been formalized; namely,we considerwhetheroptimal contractsbetween buyersand sellers deter entryand whethertheyare suboptimalfrom a welfarepoint of view.It has been pointed out by many economiststhat contractsbetween buyers and sellers in intermediategood industriesmay have significant entrypreventioneffectsand that such contracts may be bad froma welfarepointof view.3 *Department of Economics, Harvard University, Cambridge,MA 02138, and Universityof California, We are greatlyindebtBerkeley,CA 94720,respectively. ed to Jean Tirole for helpingus formulatethe model. We also thankJerryGreen and Oliver Hart for their useful suggestionsand kind encouragement.We have been most fortunateto benefitfrommanyhelpfuldiscussions with Dilip Abreu, Richard Caves, Nancy Gallini, Andreu Mas-Colell,and Eric Maskin. 1See, for example, the seminal contributionsby Michael Spence (1977) and AvinashDixit (1979, 1980). 2For a recentsurvey,see Drew Fudenbergand Jean Tirole (1986). 3Spence (p. 544), for example, brieflymentioned contracts as a method for impedingentry; see also 388

On the other hand, it is a widespread opinion among antitrustpractitionersthat contractsbetweenbuyersand sellersare soThere have been a number cially efficient.4 of antitrustcases involvingexclusivedealing contractsand oftenthe decisionreachedby the judge has lead to considerable controversy.One famouscase, UnitedStates v. United Shoe MachineryCorporation(1922), illustratesquite clearly the nature of the debate: the United Shoe MachineryCorporation controlled 85 percent of the shoemachinerymarketand had developeda complex leasing systemof its machinesto shoe manufacturers,a leasing system against which, it was thought,other machinery commanufacturerswould have difficulty peting. The judge ruled that these leasing contractswere in violationof the Sherman Act; his decision has been repeatedlycriticized by leading antitrust experts (see Richard Posner, 1976, and Robert Bork, 1978). The main argumentagainstthe decision has been expressedby Posner: "The point I particularlywant to emphasize is that the customers of United would be unlikely to participate in a campaign to strengthenUnited's monopoly position without insisting on being compensated for the loss of alternativeand less costly

thereis a literaOliverWilliamson(1979). Furthermore, tureon barriersto entryand verticalintegrationthatis relevantto our discussion,since mostof the timewhat can also be verticalintegrationachievesin thisliterature done throughan appropriatecontract.(See Roger Blair and David Kaserman,1983.) 4This position has been forcefullydefended by Robert Bork (1978), forexample.

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AGHION AND BOLTON: CONTRA CTS AND ENTR Y

(because competitive)sources of supply" (p. 203). Exactlythe same point is made by Bork (p. 140), who concludesthatwhen we find exclusivedealing contractsin practice, then these contractscould not have been signed forentry-deterrence reasons. Both Posner and Bork are rightin pointing out that the buyer is betteroff when thereis entryand thathe (she) will tend to rejectexclusivedealingcontractsthatreduce the likelihoodof entryunlessthesellercompensates him (her) by offering an advantageous deal. Nevertheless,we show thatcontracts between buyers and sellers will be signed forentry-prevention purposes. When the buyerand the sellersigna contract,theyhave a monopolypowerover the entrant.They can jointlydeterminewhatfee the entrantmustpay in orderto be able to trade with the buyer; that is to say, if the buyer signs an exclusivecontractwith the seller and then trades with the entrant,he mustpay damages to theseller.Thus he will only trade with the entrantif the latter chargesa pricewhichis lowerthantheseller's price minus the damages he pays to the seller.These damages,whichare determined in theoriginalcontract(liquidateddamages), act as an entryfee the entrantmustpay to the seller.We show that the buyerand the sellerset thisentryfeein thesame way that a monopoly would set its price, when it cannot observe the willingnessto pay of its customers.Thus, themainreasonforsigning exclusive contracts,in our model, is to extractsome of the surplusan entrantwould get if he enteredthe seller'smarket. These contractsintroducea social cost,for theysometimesblock the entryof firmsthat may be more efficient than the incumbent seller.Entryis blockedbecause the contract imposes an entrycost on potentialcompetitors.This cost takes two different forms:an entrantmust eitherwait until contractsexpire, or induce the customersto break their contractwiththe incumbentby payingtheir liquidateddamages. The waiting cost is larger,other things being equal, the longerthe contract.We are thusled to studythequestionof theoptimal length of the contract.It is a well-known principlein economicsthatif agentsengage

389

in mutuallyadvantageoustrade,it is in their best interestto signthelongestpossiblecontract.A long-termcontractcan alwaysreplicate what a sequence of short-term contracts achieves. This principle,however,sharplycontrasts empirical evidence: In practice most contractsare of an explicitfiniteduration.Many economistshave been puzzled by this obvious discrepancybetweenthe theoryand empirical evidence, and several authors have attemptedto providean explanationforwhy contractsare of a finiteduration;mostnotably Oliver Williamson(1975, 1979) and Milton Harris and BengtHolmstr6m(1983). We argue here that looking only at the lengthof a contractis misleading.What is importantis to what extenta contractof a givenlengthlocks thepartiesinto a relationship. Thus we are led to makethedistinction between the nominallengthof the contract (the lengththat is specifiedin the contract) and the effective lengthof the contract(the actual lengththatthepartiesexpecttherelationship to last at the time of signing). Liquidated damages constitutean implicit measure of the effective lengthof the contract. The paper is organizedas follows:Section I looks at optimalcontractsbetweena single buyer and the incumbentseller,when both about the partieshave the same information likelihoodof entry.SectionII analyzesoptiinmal contractswhen thereis asymmetric formationabout the probabilityof entry. SectionIII deals withoptimalcontractswhen thereare severalbuyers.Finally,SectionIV offerssome concludingcomments. 1. OptimalContracts Between One Buyer Seller andtheIncumbent We considera two-periodmodel,wherea singleproducersuppliesone unitto a buyer. The latterhas a reservation price,P = 1, and buys at most one unit. The seller faces a threatof entry,whichis modeledas follows: At the time of contractingthe seller's unit cost is c = 2' while the entrant'scost of producingthe same homogenousgood is not known. For simplicitywe assume that the in entrant'scost, ce, is uniformly distributed

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if entryoccurs and no [0,1].5 Furthermore, contract has been signed between the incumbentand the buyer,both supplierscompete in prices, so that the Bertrandequilibriumprice is givenby P = max{1,Ce). When thereis no entry,thepotentialentrant makes zero profits.Thus entrywill only occur if c_< and the probabilityof entryis givenby (1)

k=Pr(ce?<)=1

.

We attempthere to model in the simplest way the view of the world wherethereare many investorsat each period of timewho tryto investtheirfundsin themarketswhere they hope to get the highestreturns.The distributionof profitsacross markets,however,changesstochastically overtime.Therefore entryinto a givenmarketmay also be stochastic.In this storyit is implicitlyassumed that investorsdo not have an unlimitedaccess to fundsand/or thatthereare diminishingreturnsto managingmore investmentprojects. If neitherof these assumptions hold, then investmentwill take place until the marginalreturnon the last investmentproject is equal to the interest rate. Many good reasonshave been givenfor why investorsonly have a limitedaccess to funds (see for example,JosephStiglitzand AndrewWeiss, 1981, or Williamson,1971). The timingof the game is as follows:At date 1 the incumbentseller and the buyer negotiatea contract,thenentryeithertakes place or does not. Finallyat date 2, thereis productionand trade.6We assume that the

sThe choice of a uniformdistribution is entirelyfor the sake of computationalsimplicity. In our 1985 paper, we show that the qualitativeresultsobtained here are valid for any continuousdensityf(x) with a support such thatthelowerbound is finiteand thatcontainsthe interval[0 2]. 6 productiontakesplace beforeentry,theanalysis is slightlymodified.Whenthebuyerswitchesto the entrant,the incumbentmustnow incura loss of c = 21 Thus the Bertrandequilibriumin the post-entry game now is P = Ce, so thatentrywillbe precluded(since the entrantalways makes nonpositiveprofits).To avoid an outcome where ex post competition(afterentry)drives out ex ante competition(see Partha Dasgupta and Stiglitz,1984), we thenneed to assume thattheentrant

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entrant'scost, Ceo is not observablebut the partiesto the contractknowthedistribution functionof Ce* Therefore,contractscontingenton Ce cannotbe written.7 If no contract is signed at date 1, the buyer'sexpectedpayoffis givenby (2)

(1-

)

0

.1=

1

That is, with probability(1- 0) thereis no entryand the seller sets the price equal to one. Hence, the buyergetsno surplus.With probability 0, entry occurs and Bertrand competitiondrives the price down to the incumbent'sunit cost c = . Now, Posner's point simplywas that any contractthat is acceptable to the buyer must give him an expectedsurplusof at least ' (assumingthat the buyeris riskneutral).We shall showthat even thoughthe sellerfaces this constraint, there are gains to signinglong-termcontractsand in preventing entry. The buyerand the incumbentsellercould conceivablysign verycomplicatedcontracts even in thissimplesetting.For example,the price specifiedin thecontractmaybe contingenton theeventof entryor evencontingent on the entrant'soffer.8We shall, however, restrictourselvesto simplecontractsof the formc = { P, PO} and show that thereis no loss of generalityin consideringonly this type of contract.Here P is the price of the good when the buyer trades with the incumbentand PO is thepricethebuyermust

sometimesmakes losses whenhe does not enterintothe incumbent'smarket.In otherwords,the entrantsometimes has a negativeopportunitycost (see our earlier paper). 7In general,what mattersis not the actual unitcost of the entrantbut his opportunity cost of not entering. If one takesthisinterpretation, thennonobservability of the entrant'sopportunity cost is a mild assumption. One oftenobservescontractswherea retailerprovides a minimumprice warrantyof the form:"If the buyeris offereda lowerpriceby anotherretailerforthe same good, withint periods,he can thenclaimback the differencebetween the high and the low price." These are examples of contractswhichare contingenton the entrant'soffer.Of course,if such contractsare written then entryis precluded (since the entrantmakes zero profits).See our discussionof these contractsin Sec-

tionIV.

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pay if he does not tradewiththeincumbent. In other words, PO representsliquidated damages. When a contract c= {P, PO} is signed, the buyergets a surplusof 1 - P if thereis no entry.Furthermore, if thereis entry,he will only switchto the entrantif the latter offersa surplus of at least 1 - P. We shall assume that when the buyer is indifferent between switchingand not switching,he trades with the entrant.Thus in the postentry equilibrium,the buyer also gets a surplusof 1 - P. Then a contractc = { P, PO} is acceptable to thebuyeronlyif 1-P?>.

(3)

Next, an entrantcan onlyattractthebuyerif he sets a price P, such that (4)

P
(in equilibriumtheentrantsets,P = P - PO). And entryonly occurs if the entrantmakes positiveprofits: P-ce _ >.

(5)

Thus, when a contractc = { P, PO} is signed the probabilityof entrybecomes (A= max{O; P - PO}.

(6)

The incumbentnow facesthe followingprogram: (7)

max ' Po + (I - ?')(P - c), P, Po

subjectto

1- P

4.

It is straightforward to verifythat the optimal contractis thengivenby c = {t ; 2 }. There are severalconclusionsto be drawn. First, the incumbent'sexpected payoffof signingthe contractc = { 3, 2 } is given by 7= ?- 4. If he had not signed a contract, 16+ or if he had signed a contractthat completely blocks entry,his expected payoff would be '. Hence he is strictlybetteroff signingthis contractand the buyer is not worse off.

Second, when c =

391

{4 , 2 } is signed, the

probability of entryis 4'=

-2= 2 4

4 4~

Thus

the optimal contractpreventsentryto some extent but does not preclude entrycompletely. The contract c = { P, P0o} changes the entrygame in a subtleway. On the one hand, it sets a large entryfee, P0, to the entrant.This reducesthelikelihoodof entry. , does not completelyeliminate But P0= o entry,since the contractcommits the incumbent to set a price P = . Thus all entrantswithcosts Ce < ' will findit profitable to enter.Furthermore, evenif theincumbent had the opportunityof loweringthe price P below 43 in the post-entrygame, he would not want to do this.The incumbent is strictly betteroffwhenthe buyerswitchesto the entrantin thepost-entry game,forthenhe gets a surplus of 2 comparedwith a maximum surplusof P - c = 4, ifhe retainedthebuyer. By signinga contract,the incumbentand the buyerforma coalitionwhichacts like a nondiscriminatingmonopolistwith respect to the entrant.The coalitionsets P0 like a monopolistsets its pricewhenit cannotdiscriminatebetweenbuyerswithdifferent willingnessesto pay.9 If ce wereobservable,the contractcould specifyP( as a functionof ce and thecoalitionwould be able to extractall of theentrant'ssurplus(Po = 2 - Ce). The idea thattheincumbentand thebuyer can get togetherand extractsome of the entrant'srent is very general. It does not depend, forinstance,on theassumptionthat the seller sets the contract.Peter Diamond and Eric Maskin (1979) have obtained a similar result in the contextof a model of searchwithbreachof contract,whereneither the buyer nor the seller has the power of making take-it-or-leave-itoffers. Rather, Diamond and Maskin assume that the outcome of thebargaininggamebetweena buyer and a selleris givenby the Nash-bargaining solution.

9Aninteresting featureof theoptimalcontractis that if the probabilityof entryp increases,thentheoptimal price PO may decrease. For exampleif the incumbent's unitcost is k then0 = k and PO*=1-k(1-k)k/2. Thus dPo*/dk< 0 fork < 43 .

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392

Given that the incumbentand the buyer can only act as nondiscriminating monopolists, with respectto potentialentrants,the optimalcontractintroducesa social cost,for it sometimesblocks theentryof a firmwith a lower cost of productionthan the incumbent. When an optimal contract is signed,entrantswithcosts ce E [ ; 2] do not enter. To close this sectionwe explain why the buyer and the sellercan restrictthemselves to simple contracts,c = {P, PO}. The buyer and the seller can forma coalition whose value is I when theydo not allow entryinto the market(the buyer'sreservationprice is one and the incumbent'scost is c= ). They can raise theirpayoffby allowingentryand makingthe entrantpay a fee,whichin general will be a functionof the entrant'scost, ce. But the entrant'scost is privateinformation so that the coalitionfaces a revelation of informationproblem. Now, a direct mechanismwould specifya transfer fromthe entrantto the coalition,whichis a function of theentrant'scost report:t(ce). Thisfunction t(ce) mustsatisfytheincentive-compatforall ce e [0,1], ibility(IC) constraints: (IC)

7T(ce)

t(Ce)

2 7T(Ce) -t(ce)

forall Ce [(0,1]. (Where 7T(ce) is the entrant'srentwhen his cost is ce.) The IC constraintsimply that = t for all ce E [0,1]. In other words, t(ce) the entryfee is independentof the entrant's cost. Next, the entrant'srent is given by the difference betweentheincumbent'scost and his cost, ce (i.e., 7r(Ce) = - ce). The coalition chooses t to maximize: t-Pr(rzT(ce) ? t)

=

t.Pr(2

-t(

-

ce ? t)

-t).

Then the optimal transferis t*=4 and the expectedsurplusraisedis 1. Notice thatthe } also optimal contract c= {P = 4; Po= raises a surplusof 116 fromthe entrant.We can now appeal to the revelationprinciple (Dasgupta, Peter Hammond, and Maskin,

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1979), which says that no indirectmechanism does betterthanthebest directmechanism. That is, no othercontractexiststhat raises a higher surplus than 1 Therefore thecontractsto thereis no loss in restricting be of the formc = { P, P0)? II. Asymmetric Information About the Probability of Entry

In Section I it was assumedthatboth the incumbent and the buyer know the true probabilityof entry.This is not always realistic and one would expect that oftenthe incumbentis betterinformedabout thepossibilityof entrythanthebuyer.For example, if the incumbentis a high-techfirmand is the only one to have the know-howto produce a given intermediategood, then it is likely to be much betterinformedthan its customersabout the abilityof a potential competitorin acquiringthisknow-howand thus produce the intermediate good. Hence, in thissectionwe assumethattheincumbent has some privateinformation about thelikelihood of entry.1' Asymmetricinformationhas important consequences for the determinationof the optimal nominallengthof thecontract.Under symmetricinformation, thereis no incentiveforwritinga contractof finitenominal length.On the contrary,the incumbent always gains by locking the buyer into a contractin everyperiod,forthenan entrant cannot avoid payingthe entryfee by entering at a timewhenthebuyeris notbound by a contractto the incumbent.Under asymmetricinformation, on the otherhand, the seller may wish to sign a contractof finite nominal length in order to signal to the buyer that entryis unlikely.Of course,the seller could also signal his informationby

" In the above discussion we have restrictedourmechanisms.Since all agentsare selves to deterministic assumed to be riskneutral,thereis no loss of generality in considering only deterministicmechanisms (see Maskin, 1981). " One can thinkof situationswhere the buyer is betterinformedabout theprobabilityof entry.Then we problemand all the results have a classic self-selection obtained in thissectionwould also apply to thiscase.

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AGHION AND BOLTON: CONTRACTS AND ENTR Y

offeringa contract with lower liquidated damages, PO. Such a contractwould reduce the buyer's switchingcost and could only profitably be offeredby a sellerfacinga low probabilityof entry.We showhowever,that under certain conditions,signalingthrough the lengthof the contractis strictlybetter than signalingthroughliquidateddamages. To keep the analysissimple,we shall assume that the probabilityof entryis either "high" or "low." The incumbentknowsthe trueprobabilitybut thebuyerdoes not.Furthermore,as in Section I, the incumbent makes the contractoffer.The situationdescribed here is akin to an "informedPrincipal" problem (see Roger Myerson,1983, and Maskin and JeanTirole,1985). As in Section I, we shall assume that the entrant'scosts are uniformly distributedon [0,1]. The incumbent'scost, on the other hand, is either c= I or c= k, whereO < k Then the probabilityof entryis low <2. when c = k and it is highwhen c= , since when c = k, we have

information.Thus, if the moregeneralcontractsc = { p, pe, Po} are feasibleasymmeton the ric informationputs no restrictions nominallengthof thecontract. We give the followingargumentfor why such contractsmay not be feasible: First, "entry"may be a verycomplicatedeventto describe,when a firmcan enterwitha nonhomogeneous good. The incumbentmust then decide what commoditiesqualify as "entrants"and, even if a list of such commodities can be defined,an entrantwould have an incentiveto producea good whichis p > not on thatlistwhenever

pe.

Alterna-

tively,if PC > P, therewouldbe an incentive for the incumbentto claim that entryhas occurred whenever there is an ambiguity about the eventof entry.In short,the event to observe,let alone of entrymay be difficult to verify. Second, when p > pe, the buyer could bribe someone to "enter" only to forcethe incumbent to lower his price. Vice versa, when P < Pe, the incumbentmay want to bribe someone to enter. When only simple contractsc = P PO} (8) p-Pr(c?< k) =k<2 information can put are feasible,asymmetric restrictionson both the liquidateddamages and when c= -,we have PO, and the lengthof the contract.In the presentmodel, contractlengthis somewhat definedsinceproductionand trade artificially ( e <2 )=-2(9)~~+P take place only once. It should howeverbe clear fromwhat followsthattheconclusions The buyer's prior beliefs about the inreached here carryover to a model with N cumbent'scosts are givenby m = Pr(c = k). periods of production and trade (N 2 2) it is no whereentrycan takeplace in any of theseN Under asymmetricinformation, himself periods. longertruethatthesellercan restrict Here we compare the asymmetricinforwithno loss to simplecontracts,c = { P, PO}. solutionwiththeno-conIn fact,we show in our earlierpaper thatthe mation-contracting incumbentseller can achieve the symmetric tractingsolution and show that when the informationoptimal outcome by offering differencebetween high and low costs is contracts of theformc = (p, pe, po } where sufficiently large, the low-costincumbentis betteroffnot signinga contractand leaving PO is definedas in theprevioussection,P is thepricethebuyerpays ifhe tradeswiththe optionsopen untiltheentrydecisionis taken incumbentand entrydid not occur and pe by the potentialcompetitor.In a modelwith is the price the buyerpays if he tradeswith N periods,thisresultwould be modifiedand the incumbentand entrytook place. Alter- the low-costincumbentwould be betteroff natively,when the incumbentonly offers signinga shortercontractthanthehigh-cost contractsof the formc = { P, PO}, he can incumbent. information neverattainthe symmetric When the seller makes a contractoffer optimal outcome. Thus simple contracts c = c = { P, PO}, he conveysinformationabout {P, PO} are suboptimal under asymmetric his type,so that the buyer'sbeliefschange.

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THE AMERICA N ECONOMIC RE VIE W

394

p

Let the buyer'sposteriorbeliefsbe

V( c,()=V

v(c,)

= V

,B(c) = Pr(k= p/c).

(10)

The buyerwill onlyaccept thecontractif

(11) 1-P?,/(c)4/2

1-k (1-k)

I - kI - k

/

t

A

/P-O

......

3/4

V

+ (1- /3(c))I (1 - k) (11) as From(8) and (9) we can rewrite (12) 1-P2

(,B(c)/4)

+(1- 3(c))k(I-k) signsa contractc = When the incumbent ofentry is givenby { P, PO}, theprobability (13)

Pr(ce
. I:

X

II X

I

I I;I

I I

'

1/2

p**

PO

IkIk)-k/20 FIGURE 1

payoffwhenhe is Thus, the incumbent's of type0 or 4 is givenby respectively

amongthe tractforthehigh-costincumbent, class of contracts which generate beliefs B8(c) = 1. It is commonin signalingmodels (14) to obtain a plethora of equilibriaand our model is no exceptionto thisrule.Any pair 2)+P0,) = of contracts (c, c*) where c is such that (P-PO)(P,,-P+ - P0)(P0 - P + V(c, ~)=(P k)+ P - k and O Po, (otherwiseV(c,)= the diagram may be a pooling or semisepto arating equilibriumof the signalinggame. V(c,4) = P - k). It is straightforward is condition verifythattheSpence-Mirrlees Following David Kreps (1984), however,we satisfied: can refinethe Bayesian equilibriumconcept by using dominanceand stabilityarguments <0. and thussingleout thebest separatingequi(15) d/dk[- dV/dP/dV1/dPo] librium (c**, c*) where c** is definedas How is c**= {P=1-k(1-k);Po=Po*}. In otherwords,it is morecostlyfor an ofen- PO* determined?It is the solution to the probability facinga higher incumbent tryto lowerPO thanit is foran incumbent equation

of entry.Given facinga lowerprobability condition(12) we can drawFigure1 where C* =

{P =

4; Po = 2 }

is the optimalsymmet-

when0 = 4. Notice contract ricinformation willalwaysbe acceptedby thatthiscontract sidein (12) is thebuyersincetheright-hand =1 (12) beincreasingin /3and when /3 comes (16)

1- P 2.

In addition,thecontractc* is thebestcon-

V(c**,4+) =V(c*,),

as whichcan be rewritten

(17) ( P-Po )( Po-P +2)

+P-2

= 1+ 4

whereP = 1 - k(1 - k). Now PO* is the smaller root of this quadraticequation(see Figure1) and is given

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AGHION AND BOLTON: CONTRA CTS AND ENTR Y

And (22) reducesto

by (18)

((2P)-

P*

2)-

4P-3 )/2.

How does the optimalcontractforthe lowcost incumbentunder asymmetric information compare with the optimal symmetric informationcontract given by c*= (P= 1-k(l-k); Po = (2P - k)/2}? The optimal contractunder asymmetric information,c** specifiesthe same price P as c*, but it specifies lower liquidated damages: P0*< P0. It is straightforward to computethat Po*< P0 reducesto (19)

1+4k2>5k-2.

And for all 0
(1-f)(1-k)=

(1-k)

2.

(21)

V(c**,4f) = (P

where

-

Po*)(k -(P-

Po*)) + P-k,

P =1- k(l - k) P-Po*I=

4 +2

4(1 - k(l - k)) - 3 .

It remains to show that for small k, we have (22)

(23)

-k<

4+

2

+/4(l- k(1 - k))-3

which is clearly verifiedfor small k. Also, for k close to 2, (23) is not satisfied.We summarizethe above discussionin the followingproposition: PROPOSITION 1: Underasymmetric information about the probabilityof entry(or about theincumbent'scosts), the equivalently solutionis suchthat optimalcontracting (a) the high-costincumbent signs the optimal symmetric contractc* = { P information =3 4' .P0P = I2V}'

(b) the low-costincumbent eithersigns the second-bestcontract c**= {P=1-k(l-k); -=3 PO*=P-4-

4P

(when k is close to 2) or does not sign a contractat all (whenk is close to long-term zero). that (c) c** is characterized bytheproperty liquidateddamages (PO*) are lowerthan in theoptimalsymmetric information contract, c*={P=1-k(l-k);PO=P-(k/2)}

If he signs c** he gets

and

395

[4+ 24(1-k(1-k))-3]k

|+ 1k4(1-k(l-k))-3k +1-k(1-k)-k

(1-k)2

One can explain Propositionl(b) as follows. As k becomes smallerthe price P = 1 - k(1 - k) rises,whichmakes it more attractivefor the high-costfirmto mimicthe low-costfirm'sbehavior.In orderto discourage the high-costfirmfrom cheating,the low-costfirmmusttherefore increasethegap P - P = [ 1+1{(4(1 - k(1-k)) - 3)1/2]. But this is equivalent to raisingthe probability of entryafter a contracthas been signed (see equation (13)). There comes a point where4'= P - P0 > 4 = k; thatis, by raising P- P0, the low-costJfirm raises the ex post probabilityof entry(p') above the ex ante probability of entry(f) (see (23)). This essentially involves subsidizingsome inefficient entrantsto enterthemarket.The incumbent

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THE AMERICAN ECONOMIC REVIEW

then gets a negativetransferfromthe enbetterby not offertrant.He can do strictly ing any transfer(i.e., by not signinga contractat all). We have thusestablishedthatthe nominal lengthof the contractmay serveas a signal of the probabilityof entry.This resultconfirmsthe followingbasic intuition: The buyerreasonsas followswhenhe is offereda contract:"If the incumbentwants to signa contractof a long durationhe must be worriedabout entry,so thatI inferfrom this thatthe probabilityof entryis highand I will only accept to sign thiscontractif he charges a low price. If, on the otherhand, the incumbentoffersa short-term contract, he reveals that he is not much preoccupied about entry,so that I will be willing to accept a higherprice." The result obtained in Propositionl(c) implies that the social cost is smallerin the asymmetricinformationcase than in the symmetricinformationcase. That is, liquidated damages (PO*) are smallerin c** than in c*; thereforefewerefficient firmswill be keptout of themarket.It is worthemphasizing this point, since one usually thinksof as a constraintthat asymmetricinformation preventsagentsfromreachinga sociallyefficient outcome(a first-best optimum).This is a generalthemein Agencytheory(see Oliver Hart and Holmstrom,1985). Here, on the contrary,asymmetricinformation about the incumbent'scosts may actuallyforceagents to choose the socially efficientoutcome (wheneverthe conditionin (23) is verified). The informational constrainsthe asymmetry monopolypower of the incumbentand the buyer with respectto the entrant.There is of thisresult.Rememanotherinterpretation ber that the incumbentand the buyer are constrainedin thefirstplace by theinformational asymmetryabout the entrant'scosts. Then, the conclusionreachedhere is thatif thereexists anotherinformational asymmetry between the buyer and the incumbent (about thelatter'scost) thetwoinformational constraints maycanceleach otherout. This is an important observation for constraintsdo agency theory.Informational not necessarilyadd up; theymaycancel out.

JUNE 1987

III. OptimalContractswithSeveralBuyers

One may wonder to what extentthe resultsobtainedin SectionsI and II dependon the assumption that there is only one incumbentseller and one buyer?This section attempts to give a partial answer to this question. We compare in turnthe situation where there is one buyer but several incumbentsellers,and thesituationwherethere is one incumbentsellerbut severalbuyers. All the resultsestablishedin Section I are valid in each case. Moreover,new interesting featuresare introducedin the lattersituation, where a single incumbentnegotiates withseveralbuyers. Considerfirstthesituationwherethereare two or more identical sellersbut only one buyer. Then, Bertrandcompetitionessentially gives all the bargainingpower to the buyer;he getsall of thesurplusbut theform of theoptimalcontractdoes not change.The buyer sets P0 in the same way as the seller does, when the seller makes the contract offer. The interesting situationis whenthereare several buyers and one seller. In this case, the entrant'sprofitsdepend on how many customers he can serve in the post-entry game. What is crucial,however,is how the size of the entrant'spotentialmarketaffects the probabilityof entry.If theprobabilityof entryis independentofthesize of themarket. thenthecase of severalbuyersreducesto the case of one buyer.In general,however,the size of the marketwill affectthe probability of entry.For example,if the entrantmust pay a fixedcost of entry,then his average cost is decreasingin thenumberof customers served and the probabilityof entryis increasingin the numberof customers. In thislattercase, whenone buyersignsc long-termcontractwith the incumbent,he on all othei imposes a negativeexternality buyers. By locking himselfinto a long-rut relationwiththeseller,he reducesthesize o the entrant'spotentialmarketso that,ceteri. paribus, the probabilityof entry will b4 smaller. As a result,the other buyerswil have to accept higherprices.We show tha the incumbentcan exploitthis negativeex

VOL. 77 NO. 3

AGHION AND BOLTON: CONTRACTS AND ENTR Y

ternalityto extractmore (possibly all) surplus out of each buyer.In some cases, the sellercan impose themonopolyprice(P = 1) on each buyer, even though the ex ante probabilityof entryis arbitrarilyclose to one (ex ante refersto the no-contractsituation). In addition,the sellercan extractpart of theentrant'ssurplusby choosingdamages (PO) appropriately,so thatwe get the paradoxical resultthata sellerfacinga threatof entrymay be betteroffthan a naturalmonopoly. To reach this conclusion,we must push the logic of the game to its limits.This resultis thus interesting mainlyforillustrativepurposes. We will only consider the case of two buyers and one seller.'2 Both buyers are identicaland have a reservation price P = 1. The incumbentis as describedin Section I. The entranthas the same unit costs as in Section I; in addition,he may face a fixed cost of entry,F ? 0. We shall firstconsider the problem where F is strictlypositive. Then, in the absence of any contract,the entrant'sprofitis givenby (24)

7e= 2(

F.

-

Thus, the ex ante probabilityof entryis givenby (25)

? = Pr(7e 2 O)= (1-F)/2.

Suppose now thatone of the buyerssignsa wherePO= + oo. contractwiththeincumbent Then in the post-entry game,thisbuyerwill never switchto the entrant.The lattercan now hope to get at most: (26)

Ce =2-c

-F.

The otherbuyertherefore facesa lowerlikelihood of entrygivenby (27)

k=Pr(

e 2 0)

= (1-2F)/2.

More generally,wheneverone buyersignsa contract with the incumbentof the form to n buyers(n > 2) 12Wedeal withthegeneralization in our earlierpaper.

397

c = { P, PO}, the other buyer faces a new probabilityof entrygivenby (28)

=max

{

2

j

2;jF}

We will analyze the negotiationgame where the incumbentmakes simultaneouscontract offersto both buyers.The case where the incumbentmakes sequentialoffersis considered in our earlierpaper. Therewe establish that the timingof offersdoes not matter. The same outcomeis obtainedin the simultaneous offerscase as in thesequentialoffers case. The incumbentcan withoutloss restrict the set of contractsto be of the formc= P pr, Por}, where {p, P = the price a buyer must pay if he trades with the incumbentand the other contract; buyerhas signeda long-term PO= the damages a buyermust pay if he switches to the entrantand the other buyer has signed a contractwith the incumbent; pr = the price a buyermust pay if he trades with the incumbentand the other buyerdid not sign a contract; Por= the damages a buyermust pay if he trades with the entrantand the other buyer did not sign a contractwith the incumbent. It is implicitlyassumedhere thatall contractsare publiclyobservable.This is a strong assumption.In practice,all contractsare not observable. As a result,one can never be certainwhen a contractis observed,whether theredoes not exista hiddencontractwhich cancels the effectsof the observedcontract. In our model, however,the incumbenthas an incentiveto publicizeall of his contracts, as will become clear below. Thus, hidden contractsare not a problem. When the seller makes a contractoffer C= t P, PO, pr, Por} to each buyer, B1 and B2, the latter play a noncooperativegame where they have two pure strategies: " accept" and "reject." The payoffmatrixof this game is representedin Table 1. By the inchoosing pr and Porappropriately, cumbent can ensure that 4 = (1- 2F)/2.

398

THE AMERICAN ECONOMIC RE VIEW

And at the optimum the incumbent'sexpected payoffis givenby

TABLE 1-B1

Accept

Reject

1- P

1

pr

1- P

Accept (/2

Reject

1-

JUNE 1987

(/2 7/2

(32)

7=(2(P-Po)-F)(2(Po-P +2(P-

7/2

pr

(1-F 2

-

Essentially,this involveschoosing Porlarge enough so that the buyer who accepted a contractwill not switchto theentrant.Now, accept is a (weakly)dominantstrategy when (29)

1-P

24/2 = (1-2F)/4; 1-Pr>

(30)

When the incumbentoffersa contractto both buyers such that (29) and (30) are satisfied (and such that p = (1-2F)/2), the unique Nash equilibriumis for both buyers to accept the contractoffer.As a result,both buyers receivea strictlylower payoffin equilibriumthan if theyboth rejected the contract,since < Thus when thereare severalbuyersconthereis another tractingwiththeincumbent, reason why rational buyers are willing to perpetuate the monopoly position of the seller. As Steven Salop puts it, contracts " .... are valued by each buyer individually even whiletheycreatean externalcost to all other buyers" (1986, p. 273). He calls this situationa "free-rider in reverse"(emeffect phasis added). In additionto thiseffect, thesellercan set PO appropriatelyso as to extractthe maximum expected surplusfromthe entrant.To summarize,in thissimplemodel withsimultaneous offers,theset of optimalcontractsis givenby (31)

P

Po=P-P; p r< I

(1-2F) F+1 4

; por>pr+

I+F}

2)

)2

~+-

(1-2F) 2

Suppose now that F 2 2, then4 =0 and the incumbentis able to impose the monopoly price (P = 1) on the buyer. His expected payoffat the optimumis thengivenby

(33) 0/2.

+))

7J=

((I1-F

)2 /2) +

1.

betterthan Thus the incumbentdoes strictly a natural monopoly,since he can also extractsome of thepotentialentrant'ssurplus. On the other hand, when F = 0, we have +

=+=

2'

in reeffect and the "free-rider

verse" disappears, so that the two buyers case reduces to a one-buyercase, wherethe customer purchases two units ratherthan one. In otherwords,whentheprobabilityof entryis independentof thesize of themarket, competitionamongbuyersdoes not matter. Thus the principlesestablishedin the one buyer-oneseller case remainvalid when we allow for either more than one buyer or more than one seller.The analysisis somewhat incompletesince we did not deal with the several buyers-severalsellers case. The resultsobtainedin SectionI carrythroughto this more general model (see DiamondMaskin). As faras theresultsin thissection are concerned,it is likelythatsellerswillnot be able to exploit to the same extentthe effectin reverse. free-rider IV. Conclusion The principlesformalizedin thispaper are verygeneral.What is basicallyrequiredfor contractsto constitutea barrierto entryis that post-entryprofitsforthe incumbentin the absence of any contractbe lower than pre-entryprofits(and vice versa for consumers).In addition,it is necessarythatthe incumbentcannot discriminatebetweenenThis is a trantsof variouslevelsof efficiency.

VOL. 77 NO. 3

AGHION AND BOLTON: CONTRA CTS AND ENTR Y

the rathermild assumptionif one interprets cost of entry entrant'scost as an opportunity as in our earlierpaper.Throughoutthepaper we interpretedPO to be "liquidated damages," but PO may also representdown payments,deposits,collateral,futurediscounts, and benefits,etc. Thus, the analysis developed here has potentiallya wide range of applicability. Casual empiricismsuggeststhat"endogenous switchingcosts" for customersare a widespread phenomenon. In the housing market, for example, advance deposits in as serving rentalcontractscan be interpreted thisfunction(thereare,of course,also moral hazard reasons forrequiringdeposits).Paul Klemperer(1986) providesa numberof examples of endogenousswitchingcosts, like frequentflyerprograms,tradingstamps,deferredrebates by shippingfirms,etc. Also, fixedfeesin franchisecontractsmaybe used to extractsome rentfroma potentialcompetitor.The contractbetweenAutomaticRadio ManufacturingCo. and Hazeltine Research (see AutomaticRadio Manufacturing Co. v. Hazeltine ResearchInc., 1950) is a good example. AutomaticRadio had to pay a fixed fee irrespectiveof whetherit exploited the patents licensed by Hazeltine. Any new licensor thereforefaced an entry barrier equal to the amount of this fee. Anotherstrikingexampleis the case of Bell Laboratorieswhenit inventedthe transistor. competThere were otherresearchinstitutes ing with Bell Laboratories.In orderto preto publicizethe emptthem,Bell Labs offered technologyto any potentiallicensee,in exchange for a fixedfee of $25,000. This fee served the same functionas PO,in the contract above. Moreover Bell Lab's strategy was to become the industrystandard.Thus any individual licensee would have to take cost of into account the additionalswitching not being standardized(see E. Braun and S. Macdonald, 1978). Our analysis providesa rationaleforthepracticesdescribedhereand explains why rational customerscooperate practices. withfirmsin theseanticompetitive Unfortunately,the variety and potential complexity of these contractual clauses makes the task forantitrustauthoritiesvery difficult.

399

on exogenous A rapidlygrowingliterature switchingcostsis relatedto ourpresentstudy (see Klempererfora recentthoroughexposition). The welfareconclusionsobtained in fromours. thisresearchare radicallydifferent For example, in Klemperer,entrymay be socially inefficientbecause consumersdissipate the gains from entry(in terms of lowerprices and higheroutput)by incurring the socially wastefulswitchingcosts. In our model, the social cost comes frominsufficient entry;when entryoccurs it is always welfare improving.Salop also studies the effectof various clauses, such as the "meeting thecompetitionclause" or the"clause of the most favored nation" on competition. His emphasisis moreon cartelcoordination than entry prevention. In our model a " meetingthecompetitionclause" wouldpreclude entry since the entrantcould never undercut the incumbent.We have shown, however,that it is optimalnot to eliminate such clauses will Therefore, entrycompletely. purnever be adopted for entry-deterrence poses; theymay howeverbe usefulto facilitatecartelcoordination,as Salop shows,since theyincreasethe cost of pricecutting. Our theoryof contractlengthis a substantial departurefromexistingtheories.Most explanationshave emphasizedthe idea that contractlengthis determinedas a tradeoff between recontractingcosts and the costs associated with the incompletenessof the contract(see Williamson,1975,1985; Ronald Dye, 1985a; Jo Anna Gray,1976). A notable exceptionis Harrisand Holmstrom.In practice, uncertaintyabout the futureand the cost of writingcompletecontractsare without doubt importantelementsin the determinationof contractlength.The difficulty from a theoreticalperspectiveis however that uncertainty about the future and " transaction costs" are notoriouslyvague categories. If contractsare to be incomplete what contingenciesshould the parties leave out of the contract?This is a verydifficultquestion whichhas only receivedpartial answers (see Dye, 1985b, and HartHolmstrom).Explanationsof contractlength based on contractual incompletenesscrucially depend on how one answersthisquestion (see Dye, 1985b). In thispaper we have

400

THE AMERICAN ECONOMIC REVIEW

JUNE 1987

in Miniature: The History and Impact sidesteppedthe difficulty to providea story of Semiconductor based on asymmetricinformation.We beElectronics,New York: lieve that signalingaspects are importantin CambridgeUniversityPress,1978. the determinationof contractlength and Caves, Richard,E., "Vertical Restraintsin view our explanationas complementary Manufacturer-Distributor Relations: Incito the existingtheories. dence and Economic Effects,"mimeo., Harvard University, Recently,Benjamin Hermalin(1986) has 1984. developed anothertheoryof contractlength Dasgupta,Partha and Stiglitz,Joseph,"Sunk Costs and Competition,"mimeo.,Princebased on asymmetricinformation. He conton University,1984. siders a competitivelabor marketwhereinitiallyworkershave privateinformation about , Hammond,Peter and Maskin,Eric, "The Implementationof Social Choice productivitybut wherein a later stage this Rules: Some GeneralResultson Incentive informationbecomes public (for example, throughoutputobservations).He showsthat Compatability,"ReviewofEconomicStudies, April 1979, 46, 185-206. by varyingcontractlength,it is impossible Diamond,PeterA. andMaskin,Eric,"An Equifor firms to profitablyscreen out lowproductivityworkersfromhigh-productivity libriumAnalysisof Search and Breachof Contract,I: SteadyStates,"Bell Journalof workers.Ideally, a firmwantsto retainonly Economics,Spring1979, 10, 282-316. high-productivity workers, but long-term contractsare most attractiveto low-produc- Dixit, Avinash,"A Model of Duopoly Suggestinga Theory of Entry-Barriers," Bell tivityworkers.Thus, by screeningout workJournal of Economics,Spring 1979, 10, ers, the firmachievestheoppositeof whatit 20-32. wants: it offers long contracts to low,"The Role of Investmentin Entry productivityworkersand shortcontractsto Deterrence," Economic Journal, March high-productivity workers.In equilibrium, 1980, 90, 95-106. eitherfirmsofferonly short-term contracts, or they offer"trivial" long-termcontracts Dye, Ronald, (1985a)"Costly ContractContingencies," InternationalEconomic Rethat replicate the outcome achieved with view,February1985, 26, 233-50. short-termcontracts.In our model, on the , (1985b)"Optimal Length of Labor contrary, signaling (or screening) works. Contracts," InternationalEconomic ReMoreover,whenit is optimalforthelow-cost view,February1985, 26, 251-70. incumbent to sign a short-termcontract, Drew and Tirole,Jean,"Dynamic there does not exist an alternativetrivial Fudenberg, Models of Oligopoly,"in J. Lesourneand long-termcontract.One can view our exH. Sonnenschein,eds., Fundamentalsof planation and Hermalin's as dual: in his Pure and AppliedEconomics,New York: model the high-productivity sellers do not Harwood Academic Press,1986. want to be locked in a long-termcontract; Gray,Jo Anna,"Wage Indexation:A Macrohere it is the buyerwho does not want to economicApproach,"JournalofMonetary foregofutureopportunities. Economics,April 1976, 2, 221-35. Harris, Milton and Holmstrom, Bengt,"On REFERENCES the Duration of Agreements,"mimeo., IMSSS, StanfordUniversity, 1983. Aghion,Philippeand Bolton,Patrick," Entry- Hart,Oliverand Holmstrom, Bengt,"The ThePreventionthroughContractswith Cusory of Contracts,"in T. Bewley,ed., Adtomers,"unpublished,1985. vances in Economic Theory,New York: Blair,RogerD. and Kaserman, David L., Law CambridgeUniversityPress,1985. and Economicsof VerticalIntegration and and Moore,John,"Incomplete ConControl,New York: AcademicPress,1983. tracts and Renegotiation,"mimeo.,MIT Bork, Robert H., The Antitrust Paradox, New 1985. York: Basic Books, 1978. Hermalin,Benjamin,"Adverse Selection and Braun, E. and Macdonald,S., Revolution ContractLength,"mimeo.,MIT, 1986.

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AGHION AND BOLTON: CONTRACTS AND ENTRY

401

mentand OligopolisticPricing,"BellJournal ofEconomics,Autumn1977,8, 534-44. Switching Costs," unpublished doctoral JosephandWeiss,Andrew, dissertation,Graduate School of Business, Stiglitz, "Credit Rationingin Marketswith ImperfectInforStanfordUniversity, 1986. mation,"AmericanEconomicReview,June Kreps,David M., "SignalingGames and Sta1981, 71, 393-409. ble Equilibrium,"mimeo.,StanfordUniWilliamson, OliverE., "The VerticalIntegraversity,1984. tion of Production:Market Failure ConMaskin,Eric, "Randomization in Incentive siderations,"AmericanEconomicReview, Problems,"mimeo.,1981. March 1971, 61, 112-23. and Tirole,Jean, "Principals with Markets and Hierarchies:Analysis Private Information,II: Dependent Valand Antitrust New York: Free Implications, ues," lecturenotes,1985. Press,1975. Myerson,Roger B., "Mechanism Design by , "AssessingVerticalMarketRestrican Informed Principal," Econometrica, tions: Antitrust Ramifications of the November,1983, 51, 1767-97. Transaction-CostApproach,"University Posner,RichardA., Antitrust Law. An Ecoof PennsylvaniaLaw Review,April1979, 127, nomicPerspective,Chicago: Universityof 953-93. Chicago Press,1976. The EconomicInstitutions ofCapitalSalop,Steven,"Practicesthat(credibly)Facilism, New York: Free Press,1985. itate Oligopoly Coordination,"in J. StigRadio Manufacturing Co. v. Hazeltine litz and F. Mathewson,eds., New Develop- Automatic ResearchInc.,339 U.S. 827,834,1950. mentsin theAnalysisof MarketStructure, UnitedStatesv. United ShoeMachinery CorporaCambridge:MIT Press,1986. Spence,A. Michael,"Entry,Capacity,Investtion,258 U.S. 451,1922. Klemperer, Paul, " Markets with Consumer

______

_____

Contracts as a Barrier to Entry

manufacturers, a leasing system against which, it was thought, other machinery manufacturers would have difficulty com- peting. The judge ruled that these leasing contracts were in violation of the ...... An Eco- nomic Perspective, Chicago: University of. Chicago Press, 1976. Salop, Steven, "Practices that (credibly) Facil-.

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